Gaps between faces; how can I join them, without filling?
Seect the vertices you want to merge and then press Alt+M to bring up the Merge menu and select 'At Center'. Repeat for each set of vertices you want to merge.

Alternatively, if the vertices are close enough, you can select them all and use Remove Doubles (on the Mesh/Vertices menu) - increase the Merge Distance in the left-hand panel until those vertices merge together.